{
  "id": "1606.02222",
  "version": "v1",
  "published": "2016-06-07T17:13:10.000Z",
  "updated": "2016-06-07T17:13:10.000Z",
  "title": "Codes arising from incidence matrices of points and hyperplanes in $PG(n,q)$",
  "authors": [
    "Olga Polverino",
    "Ferdinando Zullo"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we completely characterize the words with second minimum weight in the $p-$ary linear code generated by the rows of the incidence matrix of points and hyperplanes of $PG(n,q)$, with $q=p^h$ and $p$ prime, proving that they are the scalar multiples of the difference of the incidence vectors of two distinct hyperplanes of $PG(n,q)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-07T17:13:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E21",
      "94B05",
      "51E22"
    ],
    "keywords": [
      "incidence matrix",
      "codes arising",
      "ary linear code",
      "second minimum weight",
      "distinct hyperplanes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}